Change in the object's kinetic energy

[UrbanXrisis]

A force acting on an object given by the function F(x)=3x^2 + 4, where F is in Newtons and x is in meters. what is the change in the object's kinetic energy as it mores from x=1 to x=3 m?

W=6x
it changes from 6 J to 18 J
the answer 12 J is not the correct one
it says 26 J

why?

 

[Parth Dave]

Why is W = 6x?

 

[UrbanXrisis]

W=F’=∫P

F(x)=3x^2 + 4
F'(x)=6x

 

[Pyrrhus]

This is what i get

$$W = \int^{3}_{1} (3x^2 + 4)\vec{i} \cdot dx \vec{i}$$

$$W = x^3 + 4x]^{3}_{1} = 34 J$$

Work-Kinetic Energy Principle

$$\sum_{i=1}^{n} W_{i} = \Delta K$$

so

$$\Delta K = 34J$$

 

[UrbanXrisis]

that's not even one of the choices. Does it matter if it was F(x) instead of F(t)?

 

[Parth Dave]

Just so you know, i believe that 26 is wrong also.

EDIT*Looks like cyclovenom got there first. The 34 is correct.

Remember, W is not F', its the other way around.

F = W'


And yes it does matter if it was F(x) instead of F(t).

 

[UrbanXrisis]

how would F be different if it was F(t)?

 

[Pyrrhus]

Just so you know, i believe that 26 is wrong also.

And yes it does matter if it was F(x) instead of F(t).

I am with Parth Dave, are you sure about this, urban?

 

[UrbanXrisis]

the packet must have a typo then

Cyclovenom, I never see you on ICQ :)